Post on 02-Jun-2018
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APPLICATIONS
Ball-and-socket joints and journal bearings are often used in
mechanical systems. To design the joints or bearings, the
support reactions at these joints and the loads must be
determined.
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SUPPORT REACTIONS IN 3-D (Table 5-2)
As a general rule, if a support prevents translation of a body in agiven direction, then a reaction force acting in the opposite
direction is developed on the body.
Similarly, if rotation is prevented, a couple moment is exerted on
the body by the support.
A few examples are shown above. Other support
reactions are given in your text book (Table 5-2).
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EQUATIONS OF EQUILIBRIUM
(Section 5.6)
As stated earlier, when a body is in equilibrium, the net force andthe net moment equal zero, i.e., F = 0 and MO = 0 .
FX = FY = FZ = 0
MX = MY = MZ = 0
The moment equations can be determined about any point.
Usually, choosing the point where the maximum number ofunknown forces are present simplifies the solution. Any forces
occurring at the point where moments are taken do not appear in
the moment equation since they pass through the point.
These two vector equations can be written as six scalar equations
of equilibrium (EofE). These are
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CONSTRAINTS AND STATICAL DETERMINACY
(Section 5.7)
A problem that is statically indeterminate has more unknowns
than equations of equilibrium.
Are statically indeterminate structures used in practice? Why
or why not? Where to get extra eqns?
Redundant Constraints: When a body has more supports thannecessary to hold it in equilibrium, it becomes statically
indeterminate.
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IMPROPER CONSTRAINTS
Having the same number of unknown reactive forces as E-o-E
does not ensure stability of a system under all loading
conditions.
In the figure, the lines of application of the reactive forces
pass through point A.
The applied loading Pwill cause the beam to rotate slightly
about point A so the beam is not properly constrained.
What does that imply?
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EXAMPLE
a) Establish the x, y and z axes.
b) Draw a FBD of the rod.
c) Write the forces using scalar equations.
d) Apply scalar equations of equilibrium to solve for the
unknown forces.
Given:The rod, supported by
thrust bearing at A andcable BC, is subjected to
an 80 lb force.
Find: Reactions at the thrust
bearing A and cable BC.
Plan:
NB: Forces parallel to an axis or pass through it create no moment about that axis
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EXAMPLE (continued)
FBD of the rod:
M X = ( MA)X + 40 (6)80 (6) = 0 ; (MA)X= 240 lb ft
M Z = ( MA)Z = 0 ; (MA)Z= 0
= 40 lb
Now write scalar moment equations about what point? Point A!
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CONCEPT QUIZ
1. The rod AB is supported using twocables at B and a ball-and-socket
joint at A. How many unknown
support reactions exist in this
problem?A) 5 force and 1 moment reaction
B) 5 force reactions
C) 3 force and 3 moment reactionsD) 4 force and 2 moment
reactions
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ATTENTION QUIZ
1. A plate is supported by a ball-and-socket joint at A, a roller joint at B,
and a cable at C. How many
unknown support reactions are there
in this problem?
A) 4 forces and 2 moments
B) 6 forces
C) 5 forces
D) 4 forces and 1 moment
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ATTENTION QUIZ
2. What will be the easiest way to determine the force
reaction BZ ?
A) Scalar equation FZ= 0
B) Vector equation MA= 0
C) Scalar equation MZ= 0
D) Scalar equation MY = 0
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